The Extended Legendre-Stirling Numbers of the First Kind

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Generating Functions for Extended Stirling Numbers of the First Kind

In this paper we extend the definition of Stirling numbers of the first kind by way of a special multiset. This results in a family of number triangles for which we show how to obtain ordinary generating functions for the rows and exponential generating functions for the columns. The latter are derived via a recursive process. We also indicate how to obtain formulas, in terms of factorials, gen...

متن کامل

The Legendre-Stirling numbers

The Legendre-Stirling numbers are the coeffi cients in the integral Lagrangian symmetric powers of the classical Legendre second-order differential expression. In many ways, these numbers mimic the classical Stirling numbers of the second kind which play a similar role in the integral powers of the classical second-order Laguerre differential expression. In a recent paper, Andrews and Littlejoh...

متن کامل

Convolution Properties of the Generalized Stirling Numbers and the Jacobi-Stirling Numbers of the First Kind

In this paper, we establish several properties of the unified generalized Stirling numbers of the first kind, and the Jacobi-Stirling numbers of the first kind, by means of the convolution principle of sequences. Obtained results include generalized Vandermonde convolution for the unified generalized Stirling numbers of the first kind, triangular recurrence relation for general Stirling-type nu...

متن کامل

Asymptotic Expansions for the Stirling Numbers of the First Kind

Let s(n,m) denote the (unsigned) Stirling numbers of the first kind: s(n,m) := [w] (w(w + 1) · · · (w + n− 1)) (1 ≤ m ≤ n, n ≥ 1). Many different asymptotic expressions for s(n,m), as n→∞, have been proposed in the literature due to their wide applications, cf. Temme [8] for a brief survey of known results together with a uniform asymptotic expansion valid for all m, 1 ≤ m ≤ n. Recently, Wilf [...

متن کامل

Congruence Problems Involving Stirling Numbers of the First Kind

It is by now well known that the parities of the binomial coefficients show a fractal-like appearance when plotted in the x-y plane. Similarly, if f(n,k) is some counting sequence and/? is a prime, we can plot an asterisk at (//,&) iff(n,k) # 0 (mod/?), and a blank otherwise, to get other complex, and often interesting, patterns. For the ordinary and Gaussian binomial coefficients and for the S...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: DEStech Transactions on Engineering and Technology Research

سال: 2016

ISSN: 2475-885X

DOI: 10.12783/dtetr/icmite20162016/4565